Active-sterile neutrino mixing is strongly constrained for m _ { s } \gtrsim 100 keV to avoid excessive energy losses from supernova cores .
For smaller m _ { s } , matter effects suppress the effective mixing angle except for a resonant range of energies where it is enhanced .
We study the case of \nu _ { \tau } - \nu _ { s } mixing where a \nu _ { \tau } - \bar { \nu } _ { \tau } asymmetry builds up due to the strong excess of \nu _ { s } over \bar { \nu } _ { s } emission or vice versa , reducing the overall emission rate .
In the warm dark matter range m _ { s } \lesssim 10 keV the mixing angle is essentially unconstrained .